Rayleigh’s, Rician’s and Gaussian’s distributed Noise Modelling for MRI Data, Stability Analysis under Parameters Variation

Abstract

Last Rayleigh’s, Rician’s, and Gaussian’s distributed noise model is obtained by using negative log likelihood minimizing. In machine learning (ML), we can implement optimization by using minimization of Negative Log Likelihood (NLL). It is maximum likelihood estimation (MLE) used the minimization of Negative Log Likelihood (NLL). The summable log – probabilities come from multiplicative probabilities. The log is used to handle very small likelihoods. The negative log likelihood comes from the need to optimize objective function (cost function or loss function). It is related to Gaussian or Rayleigh or Rician probability density functions. The noise in MRI is very critical and need to be inspected deeply for dynamical behaviour. The model amplitude of a noise – free image (I) is delayed in time due to additional disturbances (interferences). The delay parameters influence the dynamic of the system and need to be chosen for getting stable system. The stability is inspected for best performance. The nonlinear dynamic theory gives the key criteria for stable system. Integral part of the method is to track changes in system variables over time. The system dynamical behaviour can be chaotic, counterintuitive, or unpredictable. We get the specific system parameters criteria for getting disturbances reduction.